The invention relates to a method for designing the time dependence function km(t) for a given k-space trajectory km, where m stands for one or multiple of the spatial dimension indices x, y, or z, of a magnetic resonance imaging (=MRI) experiment carried out on an MRI system,
wherein the trajectory km is generated by applying a time varying waveform gm(t) of a gradient magnetic field,
the method taking into account
                the gradient magnitude limit G and        the gradient slew rate limit Sof the MRI system.        
Such a method is known from H. E. Cline, Magn. Reson. Med. 4 (2001), 1130, see Ref. [5].
Magnetic resonance imaging (MRI) is a powerful, non-invasive tool for obtaining spatially resolved information of objects, in particular parts of a body of a living human or animal.
In order to obtain the spatially resolved information of the object, it is necessary to apply encoding procedures. Typically, frequency encoding and/or phase encoding procedures are applied by means of field gradients. The desired spatial resolution corresponds to an area in k-space in a reciprocal manner while the area of interest of the object corresponds to the distance of k-space points also in a reciprocal manner. Points in k-space are accessed by applying an appropriate strength and duration of a gradient magnetic field.
In many MRI experiments, the relevant area in k-space is scanned along the Cartesian coordinates. However, this procedure can be time consuming.
In order to accelerate the scanning of the relevant area in k-space, it is also known to scan along particular k-space trajectories, such as spiral type trajectories. With the k-space trajectory, a path in k-space is provided. However, in order to define which point of the trajectory shall be accessed at which point of time, a time dependence function has to be found for a given k-space trajectory. The time dependence function defines a time varying waveform of the gradient magnetic field which is to be applied during the MRI experiment.
When deriving a time dependence function for a given k-space trajectory, it is known to take into account a gradient magnitude limit G and a gradient slew rate limit S of the MRI system used, i.e. the time dependence function may not require too extreme waveform amplitudes and variations, compare [5]. The gradient magnitude limit takes into account that the gradient hardware may only provide a field strength of the gradient magnetic field of G at maximum. Further, the gradient slew rate limit S takes into account that the gradient hardware may only change the field strength of the magnetic field gradient per time of S at maximum.
However, even when taking into account the gradient magnitude limit G and the slew rate limit S when designing the time dependence function, artifacts have been found in resulting MRI images, in particular when the k-space trajectory is of spiral type.
It is therefore the object of the invention to provide a method for designing a time dependence function for a given k-space trajectory, which allows obtaining better quality MRI images.